To know a geometric truth (e.g., that an isosceles triangle has two equal base angles), the mathematician must produce a particular spatial construction that makes the truth demonstrable
In Kant’s Critique of Pure Reason (1781/1787) (see the entry Kant’s views on space and time) the situation is more complicated or sophisticated. Kant introduced the notion of a priori knowledge in contrast to a posteriori, and synthetic knowledge in contrast to analytical knowledge to allow for the existence of knowledge that did not rely on experience (and was thus a priori) but was not tautological in character (and therefore synthetic and not analytic). The contentious class of synthetic a